In seeking physics beyond the SM to solve the baryogengesis problem, we will consider first leptogenesis [1]}. This is attractive since one scenario for leptogenesis uses the seesaw mechanism for neutrino mass generation. Sphaleron processes [2]} then convert lepton number asymmetry into baryogenesis [3]}. In such a scenario lepton asymmetry is generated first by means of decays of right handed sterile Majorana neutrinos to SM particles which freeze out at a certain temperature because of the expanding universe. This scenario has been shown to be viable[4]}, [5]}, [6]}, [3]}.
In general terms, gravity at Planck energies cannot be ignored since the gravitational coupling constant \(G_{N}\)  is of order \(M_{P}^{-2}\)  where \(M_{P}\)  is the Planck mass. At an energy scale \(E\)  the dimensionless constant is \(G_{N} E^{2}\)  and so, at least at the Planck scale, quantum gravity effects cannot be ignored. Within a string theory framework the gravitational sectorThe lowest energy states in a superstring theory are the graviton, dilation and the Kale-Ramond field [8]}. also has the Kalb-Ramond field and the presence of a Kalb-Ramond background would break CPT invariance.
From experiments there are stringent upper bounds [9]}, [10]} in the present era for CPTV. However CPTV could have been much greater in the early epoch of the universe, a possibility with consequences that we will explore. In our model we can show how the background diminishes with temperature (and hence time) so as to easily satisfy experimental constraints.
